A comprehensive experimental investigation was performed to better understand the effect of the weir geometry of a Piano Key weir (PKW) on the discharge coefficient for both free and submerged flow conditions. Experiments were conducted in a 12 m long, 0.4 m wide and 0.7 m deep rectangular glass-walled flume. The effects of the PKW geometry, including weir length and height, up- and downstream key widths as well as up- and downstream apex overhangs on the weir flow discharge coefficient were investigated, so that the governing weir head-discharge relationship resulted. In addition, on the basis of a comprehensive data set, practical discharge coefficient relations associated with the standard weir equation were proposed for both free and submerged flows over PKWs. The present correlations cover various types of PKWs. From the experimental data, optimum values of the primary dimensionless weir parameters result produce the maximum discharge efficiency.

Discharge coefficients for free and submerged flow over Piano Key weirs

A method is presented for the hydraulic design and analysis of labyrinth weirs based upon the experimental results of physical modeling. Discharge coefficient data for labyrinth weirs with quarter-round and half-round crest shapes are presented for sidewall angles ranging from 6 to 35°. Cycle efficiency is also introduced as a design aid, which compares the hydraulic performance of different cycle geometries. Geometric parameters that affect flow performance are discussed. The predictive accuracy of the design method is evaluated through comparisons to previously published labyrinth weir head-discharge data. The companion paper examines nappe behaviors that affect flow performance and presents hydraulic design considerations specific to nappe characteristics.

Hydraulic Design and Analysis of Labyrinth Weirs. I: Discharge Relationships

A new approach to improve the discharging capacity of sharp-crested triangular plan form weirs

The discharge capacity and hydraulic efficiency of a labyrinth weir can be increased with an Arced cycle configuration. An Arced geometric layout for labyrinth weirs is presented, including nomenclature for arc-specific geometric variables. Discharge coefficients as a function of HT/P for half-round trapezoidal Arced labyrinth weirs with 6 and 12° sidewall angles are also presented. The hydraulic performance of the tested Arced labyrinth weir geometries is compared to Projecting and in-channel labyrinth configurations and to an arced weir (horseshoe weir) with a half-round crest, including the effects of approaching flow conditions and local submergence. Differences between geometrically similar and geometrically comparable Arced labyrinth weirs are identified and discussed.

Arced Labyrinth Weirs

Nappe behavior should be considered in the design of labyrinth weirs to ensure hydraulic optimization and to account for potential vibrations, pressure fluctuations, noise, and flow surging. Information regarding nappe aeration conditions (clinging, aerated, partially aerated, and drowned), nappe instability, and nappe vibrations for trapezoidal labyrinth weirs on a horizontal apron with quarter- and half-round crests (6°≤ sidewall angle ≤35°) is presented. Corresponding headwater ratio ranges and hydraulic behaviors associated with nappe aeration conditions are documented and discussed to aid in labyrinth weirs design, including design options directly related to nappe behavior (e.g., crest shape, crest roughness, vents, nappe breakers, notches, and staged cycles). The effects of artificial nappe aeration (a vented nappe) on nappe behavior and discharge capacity are also discussed, including recommended placements of nappe breakers.

Hydraulic Design and Analysis of Labyrinth Weirs. II: Nappe Aeration, Instability, and Vibration

Low-head labyrinth weir control structures installed on mild sloping channels or where the channel downstream of the weir is constricting and/or heavily vegetated can experience submergence. Weir submergence occurs when the tailwater surpasses the weir crest elevation, causing an increase in the upstream driving head for a given discharge, relative to a free-discharge condition. The most familiar relationship for predicting submerged weir head-discharge relationships is likely that of James R. Villemonte, which he published in 1947 for sharp-crested linear weirs. For lack of a better alternative, Villemonte’s relation has also been applied to predicting submerged labyrinth weir performance. A new dimensionless submerged head relationship developed in this study is presented for submerged labyrinth weirs. A similar relationship is also presented for linear sharp-crested weirs. The accuracy of the submerged linear weir relationship was equivalent to Villemonte’s and is simpler to solve when working in terms...

M A Chandler

Papers

Head-Discharge Relationships for Submerged Labyrinth Weirs

Predicting Submergence Effects on Labyrinth Weirs